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SIMPLIFY using a Venn Digram or Laws of Set Algebra Pamela Leutwyler

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SIMPLIFY using. a Venn Digram or Laws of Set Algebra. Pamela Leutwyler. example 1. (A  B)  (A  B) = ____. (A  B)  (A  B) = ____. Venn Diagram:. A. B. 1. 3. 2. 4. (A  B)  (A  B) . (A  B)  (A  B) = ____. Venn Diagram:. A. B. 1. 3. 2. 4. - PowerPoint PPT Presentation

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Page 1: SIMPLIFY using

SIMPLIFY using

a Venn Digram or Laws of Set Algebra

Pamela Leutwyler

Page 2: SIMPLIFY using

example 1

Page 3: SIMPLIFY using

(A B) (A B) = ____

Page 4: SIMPLIFY using

(A B) (A B) = ____Venn Diagram:

A B12 3

4

(A B) (A B)

Page 5: SIMPLIFY using

(A B) (A B) = ____Venn Diagram:

A B12 3

4

(A B) (A B) 1

Page 6: SIMPLIFY using

(A B) (A B) = ____Venn Diagram:

A B12 3

4

(A B) (A B) 1 (1,2

Page 7: SIMPLIFY using

(A B) (A B) = ____Venn Diagram:

4

(A B) (A B) 1 (1,22,4)

A B12 3

Page 8: SIMPLIFY using

(A B) (A B) = ____Venn Diagram:

A B12 3

4

(A B) (A B) 1 (1,22,4)1 2

Page 9: SIMPLIFY using

(A B) (A B) = ____Venn Diagram:

A B12 3

4

(A B) (A B) 1 (1,22,4)1 2

1 , 2

=A

Page 10: SIMPLIFY using

(A B) (A B) = ____Venn Diagram:

A B12 3

4

(A B) (A B) 1 (1,22,4)1 2

1 , 2

=A

Laws of Set Algebra::

(A B) (A B)

Page 11: SIMPLIFY using

(A B) (A B) = ____Venn Diagram:

A B12 3

4

(A B) (A B) 1 (1,22,4)1 2

1 , 2

=A

Laws of Set Algebra::

(A B) (A B) Distributive law

A ( B B)

Page 12: SIMPLIFY using

(A B) (A B) = ____Venn Diagram:

A B12 3

4

(A B) (A B) 1 (1,22,4)1 2

1 , 2

=A

Laws of Set Algebra::

(A B) (A B) Distributive law

A ( B B) Complement Law

A U

Page 13: SIMPLIFY using

(A B) (A B) = ____Venn Diagram:

A B12 3

4

(A B) (A B) 1 (1,22,4)1 2

1 , 2

=A

Laws of Set Algebra::

(A B) (A B) Distributive law

A ( B B) Complement Law

A UIdentity Law

=A

A

Page 14: SIMPLIFY using

example 2

Page 15: SIMPLIFY using

[A ( B A )] [A B ] = ____

Page 16: SIMPLIFY using

[A ( B A )] [A B ] = ____

Venn Diagram:

A B12 3

4

[A ( B A )] [A B ]

Page 17: SIMPLIFY using

[A ( B A )] [A B ] = ____

Venn Diagram:

A B12 3

4

[A ( B A )] [A B ]

[A (1,3 A )] [A B ]

Page 18: SIMPLIFY using

[A ( B A )] [A B ] = ____

Venn Diagram:

A B12 3

4

[A ( B A )] [A B ]

[A (1,3 3,4)] [A B ]

Page 19: SIMPLIFY using

[A ( B A )] [A B ] = ____

Venn Diagram:

A B12 3

4

[A ( B A )] [A B ]

[A (1,3 3,4)] [A B ] [A (1,3,4)] [A B ]

Page 20: SIMPLIFY using

[A ( B A )] [A B ] = ____

Venn Diagram:

A B12 3

4

[A ( B A )] [A B ]

[A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ]

Page 21: SIMPLIFY using

[A ( B A )] [A B ] = ____

Venn Diagram:

A B12 3

4

[A ( B A )] [A B ]

[A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ]

Page 22: SIMPLIFY using

[A ( B A )] [A B ] = ____

Venn Diagram:

A B12 3

4

[A ( B A )] [A B ]

[A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ]

Page 23: SIMPLIFY using

[A ( B A )] [A B ] = ____

Venn Diagram:

A B12 3

4

[A ( B A )] [A B ]

[A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ]

1, 3

Page 24: SIMPLIFY using

[A ( B A )] [A B ] = ____

Venn Diagram:

A B12 3

4

[A ( B A )] [A B ]

[A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ]

1, 3 = B

Page 25: SIMPLIFY using

[A ( B A )] [A B ] = ____

Venn Diagram:

A B12 3

4

[A ( B A )] [A B ]

[A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ]

1, 3 = B

Laws of Set Algebra::

[A ( B A )] [A B ]

[(AB) (A A)] [A B ]

Distributive Law

Page 26: SIMPLIFY using

[A ( B A )] [A B ] = ____

Venn Diagram:

A B12 3

4

[A ( B A )] [A B ]

[A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ]

1, 3 = B

Laws of Set Algebra::

[A ( B A )] [A B ]

[(AB) (A A)] [A B ]

Distributive Law

[(AB) ] [A B ]

[(AB) ] [A B ]

Complement Law

Identity Law

Page 27: SIMPLIFY using

[A ( B A )] [A B ] = ____

Venn Diagram:

A B12 3

4

[A ( B A )] [A B ]

[A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ]

1, 3 = B

Laws of Set Algebra::

[A ( B A )] [A B ]

[(AB) (A A)] [A B ]

Distributive Law

[(AB) ] [A B ]

[(AB) ] [A B ]

Complement Law

Identity Law

[A B ] [A B ]

Page 28: SIMPLIFY using

[A ( B A )] [A B ] = ____

Venn Diagram:

A B12 3

4

[A ( B A )] [A B ]

[A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ]

1, 3 = B

Laws of Set Algebra::

[A ( B A )] [A B ]

[(AB) (A A)] [A B ]

Distributive Law

[(AB) ] [A B ]

[(AB) ] [A B ]

Complement Law

Identity Law

[A B ] [A B ]

( A A ) B Distributive Law

Page 29: SIMPLIFY using

[A ( B A )] [A B ] = ____

Venn Diagram:

A B12 3

4

[A ( B A )] [A B ]

[A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ]

1, 3 = B

Laws of Set Algebra::

[A ( B A )] [A B ]

[(AB) (A A)] [A B ]

Distributive Law

[(AB) ] [A B ]

[(AB) ] [A B ]

Complement Law

Identity Law

[A B ] [A B ]

( A A ) B Distributive Law

U B Complement Law

Page 30: SIMPLIFY using

[A ( B A )] [A B ] = ____

Venn Diagram:

A B12 3

4

[A ( B A )] [A B ]

[A (1,3 3,4)] [A B ] [1,2 (1,3,4)] [A B ] [ 1 ] [A B ] [ 1 ] [ 3 ]

1, 3 = B

Laws of Set Algebra::

[A ( B A )] [A B ]

[(AB) (A A)] [A B ]

Distributive Law

[(AB) ] [A B ]

[(AB) ] [A B ]

Complement Law

Identity Law

[A B ] [A B ]

( A A ) B Distributive Law

U B Complement Law

= B Identity Law

B